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Set-theoretic Analysis of Nominative Data
Authors: Volodymyr G. Skobelev, Ievgen Ivanov, Mykola Nikitchenko
Keywords: nominative set, nominative data, set theory, lattice theory, algebraic system, lower semilattice, lower and upper cones, closed intervals.
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Keywords: nominative set, nominative data, set theory, lattice theory, algebraic system, lower semilattice, lower and upper cones, closed intervals.
Abstract
In the paper we investigate the notion of nominative data that can be considered as a general mathematical model of data used in computing systems. The main attention is paid to flat nominative data called nominative sets. The structure of the partially-ordered set of nominative sets is investigated in terms of set theory, lattice theory, and algebraic systems theory. To achieve this aim the correct transferring of basic set-theoretic operations to nominative sets is proposed. We investigate a lower semilattice of nominative sets in terms of lower and upper cones, closed and maximal closed intervals of nominative sets. The obtained results can be used in formal software development.Volodymyr G. Skobelev
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
40 Glushkova ave., Kyiv, Ukraine, 03187
Phone: +38 063 431 86 05
E-mail:
Ievgen Ivanov, Mykola Nikitchenko
Taras Shevchenko National University of Kyiv
01601, Kyiv, Volodymyrska st, 60
Phone: +38044 2590519
E-mail: ,
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
40 Glushkova ave., Kyiv, Ukraine, 03187
Phone: +38 063 431 86 05
E-mail:
Ievgen Ivanov, Mykola Nikitchenko
Taras Shevchenko National University of Kyiv
01601, Kyiv, Volodymyrska st, 60
Phone: +38044 2590519
E-mail: ,
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
Fulltext
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Contents
- Convex graph covers
- Set-theoretic Analysis of Nominative Data
- Admissibility, compatibility, and deducibility in first-order sequent logics
- Small P Systems with Catalysts or Anti-Matter Simulating Generalized Register Machines and Generalized Counter Automata
- Extensionality, Proper Classes, and Quantum Non-Individuality
- Edge detection in digital images using Ant Colony Optimization
- Probability on groups and an application to cryptography
- Classification of Early Stages of NAFLD Based on Dual Diagnostic Methods
- Annotation on PhD Thesis
